A Nearly Optimal Fractional Delay Filter Design Using an Asymmetric Window

Abstract

Abstract-In this paper a numerically efficient filter design method suitable for variable fractional delay (VFD) filter implementation is investigated. We propose to use a well known window method with an asymmetric window extracted from optimal filter designed beforehand. As we will demonstrate, such an approach, if additional gain correction is applied, allows for nearly optimal VFD filter design. Thus, the proposed approach combines window method simplicity with performance comparable to that of optimal filters. Efficiency of the presented technique makes it suitable for designing filters with varying delay in real time.

Variable Fractional Delay Filter Design Using a Symmetric Window

“…Performed experiments confirmed that a good reconstruction is achieved for both parts of extracted windows [31]. In particular, for windows extracted from LS filters, there is no noticeable variation in the shape of even and odd parts of the window.…”

“…It is interesting that although in this paper we discuss only the use of symmetric reference windows, high quality VFD filters can be designed with both symmetric and asymmetric reference windows [31]. According to our research [31], using asymmetric reference window, optimal results are achieved for the selected reference delay and nearly optimal results for other delays.…”

“…According to our research [31], using asymmetric reference window, optimal results are achieved for the selected reference delay and nearly optimal results for other delays. On the other hand, a symmetric reference window offers comparable performance and additionally a half of the reference window coefficients is the same and the gain correction factor is a symmetric function of filter delay which can result in lower utilization of DSP resources.…”

“…With such a window we can design the optimal MF filter. Analogically, for LS and minimax FD filters formula (48) gives us appropriately scaled (by gain correction factor (40)) symmetric reference windows (29), which can be used for a nearly optimal filter design [6,30,31].…”